A handful of NFL teams tried to play nice Monday and put on their best face.

The Vikings politely announced that head coach Leslie Frazier “will not return” for the 2014 season. The Buccaneers “dismissed” coach Greg Schiano and general manager Mark Dominik. Redskins coach Mike Shanahan was ever-so-kindly “relieved of his duties,” as was Lions coach Jim Schwartz.

The NFL regular season was less than 24 hours in the books, and already a half-dozen teams had created coaching vacancies (without using the “F word,” of course: “fired”). Houston fired its coach three weeks ago, and Cleveland fired coach Rob Chudzinski Sunday night after just 353 days on the job.

And the carousel may not be done spinning. Tennessee coach Mike Munchak will have to wait until the end of the week to speak with Titans CEO Tommy Smith and learn his fate. The Cowboys and Dolphins sat quietly Monday but still have decisions to make.

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It’s a delicate situation, firing not only a head coach but also usually his assistant coaches and football operations employees. The head coaches will survive just fine; many will land coordinator jobs within a few weeks, and Chudzinski, who signed a four-year deal last year, reportedly will receive $10.5 million in severance, while Shanahan will collect $7 million.

But the offensive line coaches and assistant strength coaches and quality-control coaches that also get shown the door don’t have golden parachutes, and don’t know whether they’ll land another job in the NFL.

The Patriots haven’t had to deal with a coaching search in 14 years, but still can’t avoid getting caught up in the fray.

A league source confirmed to the Globe that the Browns have requested permission to interview Patriots offensive coordinator Josh McDaniels, who was the Broncos head coach in 2009-10. The Browns also want to interview another former Patriot coach, current Penn State coach Bill O’Brien, although reports indicate that O’Brien is the heavy favorite to fill the Texans’ opening.

The Browns’ interest in Patriots past and present shouldn’t come as much of a surprise: Cleveland general manager Michael Lombardi long has been a close friend and admirer of Bill Belichick and the Patriots organization.

But before you start cursing out Cleveland fans for stealing the Patriots offensive coordinator during the team’s playoff run, remember these important points:

1. No team can hire a coach without first interviewing a minority candidate, per the league’s Rooney Rule. The Browns have not fulfilled that requirement yet.

2. Just because the Browns asked for permission to interview McDaniels doesn’t mean the Patriots have to grant it. The Patriots can decide not to allow McDaniels to interview for any head coaching vacancy across the league, but they can’t be selective about it. Either McDaniels can interview for every job or none at all.

3. Because the Patriots have a bye this weekend, any team wishing to interview McDaniels has to do so by the end of Sunday’s wild-card games. But the interviews end for McDaniels as soon as the calendar turns to Jan. 6 (he could interview again in the off week if the Patriots make the Super Bowl), and he cannot accept a head coaching job until the Patriots are eliminated from the playoffs.

And while the prospect of becoming a head coach again must be alluring — there are only 32 of these jobs in the world, after all, and they tend to pay pretty well — McDaniels, 37, might want to think twice about the Cleveland job.

There are some pieces to like about the Browns — they have an electrifying receiver in Josh Gordon, good young talent on defense, and two first-round picks (the No. 4 pick and Indianapolis’s) — but this is an organization that just dumped Chudzinski after a year and will now have its fifth head coach in seven years. Owner Jimmy Haslam is still being investigated for fraud involving his truck-stop company, a probe that hangs over the team like a black cloud.

And while the Browns are decently positioned to find themselves a franchise quarterback, there’s no guarantee they will.

Two teams above them in the draft also need a quarterback (Houston and Jacksonville), and the Rams reportedly want to trade out of the No. 2 pick, which could allow another team to leapfrog the Browns for a quarterback. Jay Cutler might be available; it’s still unknown whether he will return to the Bears or whether the Browns think he’s worth the commitment.

Maybe if McDaniels could look into his crystal ball and see who his quarterback would be with the Browns in 2014, then the job would be intriguing. Otherwise, there is too much uncertainty at quarterback and too much of a circus-like atmosphere to make it an attractive job. McDaniels has a good thing going in New England and can remain patient if he so chooses.

Elsewhere around the league, teams won’t waste much time filling vacancies, as most like to have their new coaching staff intact by the time Senior Bowl week starts Jan. 19.

The Bucs appear to have zeroed in on former Bears head coach Lovie Smith, who was Tampa Bay’s linebackers coach for five years under Tony Dungy and could help win back the Bucs locker room after Schiano nuked it with his demanding style. Smith reportedly would bring in former Cal coach Jeff Tedford as his offensive coordinator, and his former boss with the Bears, Jerry Angelo, could replace Dominik as Bucs GM.

A Miami team source told the Globe there was a lot of nervousness in the building Monday following the team’s supremely disappointing finish to the season: after beating the Patriots to improve to 8-6, they lost to the Bills and Jets to miss out on the playoffs.

The feeling internally is that the Dolphins should have been a 10-win team this year, and accountability is coming, although offensive coordinator Mike Sherman and offensive line coach Jim Turner appear to be in much more danger than head coach Joe Philbin. The status of GM Jeff Ireland is unclear, although he is signed through next season.

Three popular names that popped up Monday are Seattle defensive coordinator Dan Quinn, Denver offensive coordinator Adam Gase, and Arizona defensive coordinator Todd Bowles, all of whom are drawing interest from Minnesota and Cleveland. The Redskins may also be showing interest in Bengals offensive coordinator Jay Gruden, who has a relationship with GM Bruce Allen.

But Gruden’s brother, Jon, seems content to stay in the TV booth another season.

“I don’t want to be considered for any of these jobs,” Jon Gruden told the St. Paul Pioneer Press. “I’m hoping to do the best I can to hang on to my job.”

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